Modelling of flows in a petroleum reservoir is essentially based on the application, to the previously gridded reservoir (or to a portion thereof), of the well-known Darcy's law describing the flow of fluids in porous media, of the law of mass conservation in each volume unit, of the thermodynamic relations that govern the evolution of the phase parameters of the fluids such as viscosity, density, on initial conditions, on structural closure boundary conditions and on bottomhole conditions.
The <<Black Oil>> model, referred to as B.O. hereafter, is one of the most commonly used models in petroleum simulation. It allows to describe a compressible three-dimensional and three-phase (water-oil-gas) flow. The petroleum effluents involved in this model are generally described by a water constituent and by two constituents for the reservoir fluid, the term constituent covering here the notion of component (such as H2O for water) and the notion of pseudo-component (group of components). The constituents involved in this model are three in number: a water constituent (E), a heavy hydrocarbon constituent (L) and a light hydrocarbon constituent (V). In a B.O. type model referred to as <<strict>>, constituent (E) is present only in the water phase, constituent (L) is present only in the liquid hydrocarbon phase (referred to as oil or condensate), and constituent (V) is distributed among the liquid and vapour hydrocarbon phases (phase referred to as gas). Although the use of B.O. models is not recommended in certain condensate gas cases, it is however applicable to a large number of industrial cases.
Another well-known simulation model, referred to as <<compositional>> model, is also used, wherein the hydrocarbon fluids are represented by a larger number of components, at least three, often more. Modelling the flows of these more detailed fluids leads to very long computing times (much longer than those required for B.O. type modelling) as a result of the larger number of constituents, but also because it is often necessary to reduce the size of the grid cells to limit numerical errors and consequently to increase the number of cells.
For practical reasons, the fluids in place are described as consisting of a number of components or pseudo-components that is much smaller than the real number of components, so that the modelling computations can be carried out within a reasonable period of time. A composition reduced to some 5 or 10 pseudo-components is generally sufficient to represent the behaviour of the fluids in the reservoir.
Patent application WO-99/42,937 and the paper by C. Leibovici and J. Barker <<A Method for Delumping the Results of a Compositional Reservoir Simulation>>, SPE 49068, presented at the SPE Annual Technical Conference and Exhibition New Orleans, 27–30Sep. 1998, describe a method for predicting the evolution of the detailed composition in time, from computations carried out in a compositional type simulation of fluids described by a certain reduced number of pseudo-components (principle of <<lumped>> representation obtained by means of a <<lumping>> operation), the number of components being at least three. The method thus allows to predict the results that would have been obtained with a reservoir simulation using a finely detailed model where the fluids are represented by a larger number of components. This operation is well-known to the man skilled in the art as <<delumping>>.
The principle of the prior delumping stage consists in calculating coefficient ΔD0 and the n coefficients ΔDp (i.e. n+1 coefficients, n being the number of parameters of the equation of state) of a known general equation, previously published in a paper by C. F. Leibovici, E. H. Stenby, K. Knudsen, <<A Consistent Procedure for Pseudo-Component Delumping>>, Fluid Phase Equilibria, 1996, 117, 225–232:                               Ln          ⁡                      (                          k              i                        )                          =                              Δ            ⁢                                                  ⁢                          D              0                                +                                    ∑                              p                =                1                            n                        ⁢                          Δ              ⁢                                                          ⁢                              D                p                            ⁢                              Π                pi                                                                        (        1        )            where the Πpi, are fixed characterization parameters of constituent i in the equation of state for a given thermodynamic representation, from the equilibrium constants kl of each constituent of the lumped thermodynamic representation computed during compositional simulation in each grid cell and at each time interval. If Nrg is the number of components of the lumped thermodynamic representation, we thus have Nrg equations to determine n+1 coefficients. A necessary condition is therefore that Nrg is at least equal to n+1. For Peng-Robinsons's two-parameter equation of state, a lumped thermodynamic representation with at least three components is therefore required.
Once coefficient ΔD0 and the n coefficients ΔDp calculated, they are used for calculating the equilibrium constants of the components of the detailed thermodynamic representation (Nrd components) by applying Equation (1) to the Nrd components with their own fixed characterization parameters in the detailed thermodynamic representation.
By using a) the equilibrium constants thus determined for the detailed thermodynamic representation, b) the flows between each grid cell and in the wells, c) the vapour fraction in each grid cell from the lumped compositional simulation, and d) the global detailed composition in each grid cell and in the injection wells at the beginning of each time interval, the detailed composition of each hydrocarbon phase at the time interval t and the global detailed composition of each cell at the next time interval (t+1) are then estimated in each cell.
One of the advantages of this method is that it is not necessary, in the delumping stage at each time interval, to solve the equation of state, whether for the lumped representation or for the detailed representation, which allows to save computing time. One drawback of the method is that it is not applicable to B.O. type simulations since convenient equations of state have at least two parameters.
Patent application WO-98/5,710,726 describes a method for predicting the evolution of the detailed composition in time from the flow computations carried out in a B.O. type simulation where the hydrocarbon phases are described by only two components (L) and (V). The drawback of this method is that it requires the use of the equation of state of the detailed representation at each time interval, and it is therefore time-consuming during the delumping stage.